Grasp and Manipulation of Five Fingered Hand Robot in Unstructured Environments

GANIPINENI SAI KRISHNA Int. Journal of Engineering Research and Applications www.ijera.com
ISSN : 2248-9622, Vol. 4, Issue 12( Part 3), December 2014, pp.97-102
www.ijera.com 97 | P a g e
Grasp and Manipulation of Five Fingered Hand Robot in
Unstructured Environments
GANIPINENI SAI KRISHNA*, VENKATA RAMANA NYNALA**
*,**Mechanical Engineering, QIS College of Engineering and Technology, Ongole - 523272, India
Abstract—
Handling of objects with irregular shapes and that of flexible/soft objects by ordinary robot grippers is difficult.
It is required that various objects with different shapes or sizes could be grasped and manipulated by one robot
hand mechanism for the sake of factory automation and labor saving. Dexterous grippers will be the appropriate
solution to such problems. Corresponding to such needs, the present work is towards the design and
development of an articulated mechanical hand with five fingers and twenty five degrees-of-freedom having an
improved grasp capability. Since the designed hand is capable of enveloping and grasping an object
mechanically, it can be conveniently used in manufacturing automation as well as for medical rehabilitation
purpose. This work presents the kinematic design and the grasping analysis of such a hand.
Keywords :Dexterous hand,forward kinematics,simulation,force closure
I. INTRODUCTION
Dexterous multi-fingered hands represent an
interesting research area. Two of the major issues in
the area are; design of more dexterous hand, and its
grasp capability including quality of grasp. These
research topics are technological and scientific
challenges. Up to the present time, a number of multi-
finger hands have been developed. However, there
has been little work pertaining to the planning of
grasp for the fingers together which behave as several
cooperating robots. Review of past work[1-5] shows
that different researchers tried different type of
models for multi-fingered hands with multiple fingers
and each having multiple degrees of freedom (DoFs)
to mimic the real human hand. During the past two
decades, closure properties, including form-closure
and force-closure, have been extensively studied in
robotic grasping. A grasp is said to be form-closure if
the object in any motion collides with the contacts,
while a grasp is said to be force-closure if the contact
forces can equilibrate any external wrench. Form-
closure as explained by Bicchi [4] is related only to
the object geometry and the contact positions. It can
be considered as a pure geometric property. On the
other hand, Nguyen [5] presented that form-closure
and force-closure are dual to each other. He
suggested the problem of synthesizing planar grasps
that have force closure. A grasp on an object is a
force closure grasp if and only if we can exert,
through the set of contacts, arbitrary force and
moment on this object. Equivalently, any motion of
the object is resisted by a contact force that is the
object cannot break contact with the finger tips
without some non-zero external work. Bounabet.
al.[6] developed a new necessary and sufficient
condition to achieve equilibrium and force closure
grasp using grasp wrench central axis method. They
also presented an algorithm for computing force-
closure grasps with n-hard fingers contact with
coulomb friction model. Kraget. al.[7] suggested an
algorithm for the efficient computation of
independent contact regions for grasping an object,
under the assumption that a user input in the form of
initial guess for the grasping points is readily
available. The suggested method discretized 3D-
objects with any number of contacts and can be used
with any of the following models: frictionless point
contact, point contact with friction and soft finger
contact. Suhaibet. al.[8] presented the optimization
method to obtain the most stable grasp for a
nominated set of contact points and they developed
an algorithm to calculate the equilibrating forces.
They also optimized the value of friction angles so as
to satisfy the condition of stable grasp.
The objective of the present work is to
kinematically design a multi-fingered dexterous
robotic hand that is capable of compliant handling of
objects and to analyze its manipulating capability in
the context of the afore-mentioned application
domains and to seek an appropriate model through
kinematic and grasp analysis. The work consists of
two parts. Firstly a kinematic simulation of the
fingers and the complete hand is carried out to
determine the dexterity and workspace. Secondly, the
grasp analysis is carried out to assess the force
closure grasping capability of the hand. In the present
work a hand model is proposed with 5 fingers and 25-
DoFs, which includes 2-DoFs at CMC joint of ring
finger, little finger and thumb. These 6-DoFs
contribute to motion of the palm arch. The wrist is
considered as the origin of global reference plane,
and hence it is assumed to be a fixed point thereby
RESEARCH ARTICLE OPEN ACCESS

the two degrees of freedom which provides motion at
wrist in real human hand are restricted in this study.
A detailed study on the force closure grasping
capability and quality has been carried out. The
workspace of the five fingered hand has been used as
the maximum spatial envelope. The problem has been
considered with positive grips constructed as non-
negative linear combinations of primitive and pure
wrenches. The attention has been restricted to
systems of wrenches generated by the hand fingers
assuming Coulomb friction. In order to validate the
algorithm vis-a-vis the designed five fingered
dexterous hand, example problems have been solved
with multiple sets of contact points on various shaped
objects.
II. MODELLING OF HAND
Since multi-fingered robot hands are designed to
emulate the human hands, most anthropomorphic
robot hands duplicate the shape and function of
human hands. The size of the hand is a significant
part in the research. The hand can be directly attached
to the end of an industrial robot arm or play a role in
the prosthetic applications. The structure of the
fingers and other regions of human hands is almost
the same and independent, as shown in Fig.1. The
finger segments in human hand give us the
inspiration to design an independently driven finger
segment to construct a whole finger. The segmental
lengths of the thumb and fingers are taken
proportionately to hand length and hand breadth with
a fixed wrist. Typically the hand mechanism is
approximated to have 27 DoFs, which consists of 25
DoFs at different joints of the fingers and 02DoFs at
wrist. In the present study the wrist is considered as a
fixed origin. Hence, only 25 DoFs are considered.
The thumb is modeled with 5 DoFs. The index and
middle fingers are modeled with 4 DoFs each. The
ring and little fingers are modeled with 6 DoFs each,
considering two degrees of freedom each at CMC
joint for palm arch. The Trapeziometacarpal (TM)
joint, all five Mecapophalangeal (MCP) joints and
two CMC joints are considered with two rotational
axes each for both abduction-adduction and flexion-
extension. The Distal-Interphalangeal (DIP) joints on
the other four fingers possess 1 DoF each for the
flexion-extension rotational axes. The thumb and
other fingers’ parameters are tabulated in Table 1 and
Table 2 respectively.
A simulation study of the kinematic model of the
hand is carried out to test and validate the design and
to consolidate the result considering the anatomy and
anthropometric data of human hand. The joint limits
are also considered for different joint based on
literature [5]. A kinematic model, characterized by
ideal joints and simple segments, is developed to
calculate the fingertip position as well as the work
space. Given the joint angles, the fingertip position in
the palm frame is calculated by the kinematic model.
The Denavit-Hartenberg (DH) method is used to
represent the relation between the coordinate systems
and to determine the DH parameters for all the
fingers. The global coordinate system for hand is
located in the wrist assuring the transfer from a
reference frame to the next one the general expression
of the matrix. The transfer matrices are written for all
fingers
separately.
Fig.1. Kinematic model of human hand.
A. Anthropometry Data and Joint Limits
The hand joints under design are similar to those
of the human hand. However the joints considered for
the dexterous hand consist of the metacarpal joints
present in the palm connecting to the fingers and the
joints right on the fingers. In order to make the
dexterous hand similar in construction and in function
to that of a human being, the links between the joints
are taken proportional to their respective bones in a
human hand. The parameters used to know the bones’
lengths are hand length (HL) and hand breadth (HB)
which are different for every person. In the present
work it is considered that the individual fingers are
like open link manipulators, hence each segment of
the finger is considered as a link. The length of
segments is important to finding the finger tip position
and finally the work envelope of a particular hand
model. The segment lengths are also different for
different hands. It is required to generalize the
proportion of each segment with the hand parameters,
so that for a particular hand the individual segment
lengths can be calculated. For the purpose of our
model, the anthropometric data of a typical male
human hand has been considered [9, 10]. Similarly the
degrees of freedom and angle limits for motion have
been emulated in the hand model to make it dexterous.
The anthropometric data for the palm( metacarpal
region) are presented in table-1, where as that of
fingers (phalangeal region) are presented in table 2,
where HL and HB are the length and breadth of the
hand respectively.

Table 1Segment length for metacarpal bones
Locating the Finger Tip:
A kinematic model is developed to calculate the
fingertip position. Given the joint angles, the fingertip
position in the palm frame is calculated by the
kinematic model. The DH parameters for all the
fingers are determined. The coordinate systems are
located along each joint; a global coordinate system
for hand is located in the wrist as shown in Fig.1. The
general expression of the matrix can be written as
follows:
cos i sin i cos i sin i sin i Li cos i 

sin  cos  cos  cos sin  L sin  
i1T   i i i i ii i 
i  0 sin  cos d  (1)
 i i i 
 0 0 0 1 
 
By multiplying the corresponding transfer matrices
written for every finger, the kinematic equations
describing the motion of the fingertips with respect to
the general coordinate system can be determined.
III. MOTION SIMULATION
A computer program using these equations in
MATLAB-7.9 is developed to capture the motion of
the fingers. Every joint variable range is divided to a
finite number of intervals in order to have enough
fingertips positions to plot the spatial trajectories of
the fingertips. The workspace is obtained by
connecting these positions and the complex surface
bordering the active hand. The complex surface could
be used to verify the model correctness from the
motion point of view, and to plan the hand motion
thereby avoiding the collisions between its active
workspace and obstacles in the neighborhood. Using
Eq.1along with the parametric data of human fingers
presented in Table 1 and Table 2 the surface described
by each fingertip is generated as shown in Fig.2.
Fig.2 Workspace of the five fingers with wrist joint as
the reference
IV. FORCE-CLOSURE SPACE OF HAND
The contact space is the space defined by N
parameters that represent the grasping contact points
on some given edges of an object. The force-closure
space (FC-space) is the subset of the contact space
where FC grasps can be obtained. A methodology to
obtain the FC-space as the union of a set of convex
subspaces is presented in this section. Besides, the
approach developed here determines additional
information on the finger forces that is quite useful in
the determination of the independent regions.Fig.3
shows the space (convex hull) of the hand which
decides the size of the object that can be grasped. The
outermost circle shown in dotted line in the figure is
the convex hull of the hand. The other figure inside
the circle are the objects that can be grasped within
the given size range. The parameters used in this
paper to define the contact space are the torques
produced by unitary normal forces when frictionless
contacts are considered and the torques produced by
the unitary primitive forces when friction contacts are
considered. If the object is able to resist that pull
force or some external force then we can define that
object is in force closure condition.

Fig.3. The convex hull of the hand
IV.I GRASP ANALYSIS
We restrict our attention to systems of
wrenches generated in a plane of the Cartesian space
by hard fingers and assume Coulomb friction. The
wrench associated with a hard finger located at a point
x and exerting a force f is the zero-pitch wrench.
Wrench is basically a single force applied along a line
combined with torque. Any system of forces on rigid
body can be described with wrench. Force and
moment are encoded in wrench as:
The force equilibrium:
Fi Cos θi, Fi Sin θi : The magnitudes of finger force
Fi
di: The position vector of ith
finger
The moment equilibrium:
dix = Perpendicular distance of y component force
diy = Perpendicular distance of x component force
IV.II CONTACT MODELS
Several kinds of contact models are present for
object grasping. The two main aspects that need to be
taken into the account are the friction between the
finger and object and the property of the finger (soft
or hard). On this basis contact model can be: (i)
Frictionless point contact (FPC), (ii) Point contact
with friction (PCWF), and (iii) Soft finger contact
(SFC). Frictionless point contact is the contact model
in which there is no friction between the finger and
the object. Hence the force applied is always in the
direction normal to the surface of the object. In point
contact with friction, there exists friction between the
finger and the object. By using the Coulomb friction
model, the amount of force a contact can apply in the
tangent directions to a surface as a function of the
applied normal force can be determined. With
friction, all forces lie within the friction cone. Soft
finger contact is like point contact with friction.
Additionally, there is a torque around the normal
applied force in the contact point. In the example we
have considered point contact with friction with µ=
0.2 to 0.4, which is common for material such as
plastic and metal. The force applied by finger at
contact must lie within the friction cone, centered
about the surface normal.
IV.III CONDITIONS FOR FORCE –
CLOSURE GRASP
This work considers that there exists friction
between the objects and the finger to hold the object
firmly and to avoid slippage. The external force that
can be resisted by the finger depends upon the angle
at which the fingers are positioned on the object.
Accordingly the finger forces are decided. With a set
of contact forces, the resultant force and moment
produced should be zero while the friction condition
is satisfied. The first condition is that the body should
be in force equilibrium condition. i.e, Fx  0 &
Fy  0. The second important condition is that the
body should be in Moment (Torque) equilibrium
condition. i.e, M ox  0 & M oy  0 . The
grasp satisfying these conditions is a force closure
grasp and the object is said to be in force closure
condition. The other condition is that all the forces
that are acting on the body should not be equal to
zero simultaneously.
V FORCE CLOSURE CONDITION
FOR DIFFERENT OBJECTS
In order to check the force-closure condition of
the designed hand, objects of various shapes, sizes
and weights are checked theoretically. The sizes and
weights of the objects were chosen in a way so that
they remain within the workspace limits and payload
limit of the hand respectively whereas the shapes are
considered to be regular geometric ones. Multiple
sets of incident angles are chosen within the specified
limits of the individual fingers. In the present paper
only two objects are presented for the benefit of the
readers. The incident angles considered in these
examples are:
1  20o
; 2  25o
; 3  30o
; 4  0 o
; 5  10o
The other pertinent data are: value of coefficient of
Coulomb’s friction, µ = 0.25 (plastic and metal),
weight of the body = 100gm (0.98N), Ft  µN, where,
Ft = Tangential force and N = Normal force. In
present case Ft = 0.98N.
V.I CYLINDRICAL OBJECT
Referring to Fig.4 the maximum normal force
(N)

required, can be calculated as follows:
0.98  0.25Fn, 0.98/0.25  Fn, Fn  3.92N
Dividing this normal force in two equal parts and
applying them on the two faces of the object. i.e.
3.92/2 = 1.96N force on the LHS face and 200N force
on the RHS face.
Fig.4 Finger-tip forces on a cylindrical object
For Force Equilibrium: The force F1 can be
calculated as: F1cos 30= 1.96, hence, F1 = 2.263N.
By hit and trial method we can calculate the values of
all the forces. Hence, F2=0.490N, F3 = 0.5687N, F4
= 0.4883N, F5 = 0.5883
0.98N
For Moment Equilibrium: Considering the
moment of first finger w.r.t. point “O”, we get, M = F
*d , where, M = Moment, F = Force, d =
Perpendicular distance.
M1 = F1cos 30 *0.025 = 1.96*0.025 = 0.0686Nm.
Now this clockwise moment should be balanced by
the other four fingers on the other side of the face.
Similarly the moment generated by the forces through
other fingers can also be determined. Substituting the
values of forces already obtained we get, the values
of y coordinates as: y1 = 0.051m, y2 = 0.042m, y3 =
0.032m, y4 = 0.028m
These are the y coordinates of the four fingers in RHS
face. So the contact points are: P2 = (0.05, 0.051), P3
= (0.05, 0.042), P4 = (0.05, 0.032), P5 = (0.05, 0.028)
Hence at this position we get the moment
equilibrium. Now as the body is both under force and
moment equilibrium, the body is in force-closure
condition.
V.II TREPIZOIDAL OBJECT
Referring to Fig-5the maximum normal force
(N) required, can be calculated as follows:
0.98  0.25Fn, 0.98/0.25  Fn, Fn  3.92N
Dividing this normal force in two equal parts and
applying them on the two faces of the object .i.e.
3.92/2 = 1.96N of force on the LHS face and 200N of
force on the RHS face.
With Ft = 0.98N, the maximum normal force (N)
required, can be calculated as follows:
0.98  0.25N or 0.98/0.25  N or N  3.92N
0.98N
Fig.5 Finger-tip forces on a pyramidal object
Dividing this normal force in to two equal parts and
applying them on the two faces of the object we get,
1.96N force on the LHS face and 1.96N force on the
RHS face.
For Force Equilibrium: The force F1 can be
calculated as: F1cos 30 = 1.96, hence, F1 = 2.264N
In a manner similar to the previous one, the values of
all the forces are determined. Therefore, F2 =
0.4707N, F3 = 0.5883N, F4 = 0.3922N, F5 = 0.5393N
Summation of all the forces in RHS face is : 0.4707 +
0.5883 + 0.3922 + 0.5393 = 1.9905 N
Here the forces on LHS & RHS faces are almost
equal and we can say that the body is in force
equilibrium.
For Moment Equilibrium: In the case of pyramid
condition, the first finger on the LHS face is placed
approximately at the center of the face and the 2nd
and the 5th finger are placed randomly towards the
corner of the RHS face. The 3
rd
and 4
th
fingers are the
manipulative finger and placed normally to the RHS
face which is used to balance the moment.
Therefore total clockwise moment = 0.0741Nm, and
the total anticlockwise moment =0.03617Nm. Here
the clockwise moment exceeds the anti-clockwise
moment by 0.03617Nm.
This clockwise moment can be balanced by the 3
rd
and 4
th
finger as they will produce anticlockwise
moment and the calculation is as follows:
F3 * y1 + F4 * y2 = 0.03167
We can calculate the position of the 3
rd
and 4
th
finger
as y3 = 0.053, y4= 0.016
The positioning this finger at the given point the body
will be in moment equilibrium. Hence as the body is
in force as well as moment equilibrium we can say
that the body is in force closure condition. In a
similar manner the force–closure conditions for
objects of other geometrical shapes can be
determined.

VI RESULTS AND ANALYSIS
The effect of incident angle on the contact force
is shown in Fig.6 (a) while Fig.6 (b) shows the
variation of the force value with different values of
coefficient of friction. As the angle of force is
increased the force required to grasp the object is
increased. So the best condition is that the force
should be applied normally to the object so that the
force required by the finger is minimum. As the
coefficient of friction is increased the force required
by the finger is decreased. So we should choose the
coefficient of friction (the finger-object interface)
according to the necessity of the work.
Fig.6The effect of angle and co-efficient of friction
on the applied force by finger
VII CONCLUSIONS
The present work aims at developing a kinematic
model of a 5-fingered dexterous robotic hand with 25
degrees-of-freedom which may find its potential
applications in industries and other work places for
manipulation of irregular and that of soft objects. The
conceptual design has been done keeping human
hand’s anatomy in mind so that it has the flexibility
close to the human hand and the kinematic behavior
is similar to that of the human hand. The model
considers five fingers that are essential for grasping
and manipulating objects securely. The joints, links
and other kinematic parameters are chosen in such a
way that they represent those of a human hand. The
simulation result is very encouraging for the
prototype development of the hand. The kinematic
simulation is carried out to estimate the work volume
and assess kinematic constraints of the
conceptualized hand. The algorithm used in this work
for computing force closure grasp of arbitrary objects
is simple and needs little computational complexity
as compared to linear programming schemes. Hence
it can be conveniently used in real-time, multi-
fingered grasp programming.
REFERENCES
[1.] Bounab, B., Sidbore, D., and Zaatri, A.,
“Central Axis Approach for computing n-
Finger Force Closure Grasps.”, proceedings of
IEEE INTERNATIONA CONFERENCE ON
ROBOTICS AND AUTOMATION, pp. 1169-
1174, 2008.
[2.] Krug, R., Dimitrov, D., Charust, K., and
Lliev, B., “On the Efficient Computation of
Independent Contact regions for Force
Closure Grasps.”, Proceedings of IEEE/RSJ
INTERNATIONAL CONFERENCE ON
INTELLIGENT ROBOTS AND SYSTEMS,
pp. 586-591, 2010.
[3.] Suhib, M., Khan, R. A., and Mukharjee, S.,
“Contact Force Optimization for Stable Grasp
of Multi-finger Robotic Grippers”,
Proceedings of the WORLD CONGRESS ON
ENGINEERING, Vol. 2192, (No.-1), pp.
2194-2197, 2011.
[4.] Parida, P. K., Biswal, B. B. and Thatoi, D.
N., “Kinematic Analysis of a Anthropomorphic
Robot Hand”, Applied Mechanics and
Materials, Vols. 187, pp. 293-297, 2012.

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